In communication systems, it is advantageous to transmit and receive signals with little or no distortion so that all of the information in the signal can be preserved and processed. It is not desirable to introduce spurious signals that can mask or distort the original signal. Additionally, large signal peaks or spikes that can create excessive frequency deviation when the signal is modulated or that can saturate a system and produce harmonic distortion are not beneficial. Thus, the ability to perform non-linear operations, such as limiting the magnitude of the signal, is desirable, providing the non-linear operation does not introduce spurious signals.
The prior art, as shown in FIG. 1 in conjunction with FIG. 2, illustrates some inherent problems when processing signals. In FIG. 1, the signal 100 contains all of its information in the carrier frequency 102. In FIG. 2, the nonlinear operation of limiting is performed on the signal 100, introducing undesirable harmonics 206, 208, and 210 along with higher order harmonics. In the analog domain, the harmonics 206, 208, and 210 are removed with a low pass filter 212, which passes the primary frequency band, including the carrier frequency 102, but filters out the higher order harmonics. However, analog implementations are generally larger, more costly, and consume more power than their digital counterparts.
In portable communication systems, size, cost, power, flexibility, and repeatability are paramount concerns; consequently, digital implementations are desirable.
In the digital domain, all harmonics whose frequency is greater than half the sampling rate alias, or "fold over", into the primary frequency band, leading to severe distortion. If the initial signal is band limited to -W, W!, then digital processing can be performed at a rate, 2W. If a digital signal has an initial frequency, f, then the non-linear operation of limiting the signal produces harmonics at frequencies mf, m being an odd integer. Certain harmonics, as determined in equation 1, fold-over or produce an alias of that harmonic in the primary frequency band -W, W!.
(1) Alias =.vertline.mf+2kW.vertline.&lt;W PA1 m=odd integer PA1 f=initial frequency PA1 k=any positive or negative integer PA1 W=primary frequency band -W, W! PA1 2W=sampling frequency or rate
In FIG. 3, the prior art illustrates the effects of non-linear operations on an input signal 310 with a frequency of 3 kHz. With a bandwidth of .+-.4 kHz and a sampling rate of 8 kHz, the third harmonic 312 folds over into the primary frequency band at 1 kHz; consequently, the third harmonic cannot be removed with a low pass filter. Because the third harmonic is only 15 dB down, it leads to significant and undesirable distortion.
Accordingly, there is a need to provide a low cost, small size, and low power digital processor for reduced distortion and frequency deviation.